Use the appropriate compound interest formula to compute the balance in the account after the stated period of time
​$20 comma 000 is invested for 6 years with an APR of 3​% and daily compounding.
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Part 1
The balance in the account after 6 years is ​$
  
enter your response here.
​(Round to the nearest cent as​ needed.)

To compute the balance in the account using the compound interest formula with daily compounding, we use the following formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the final amount (balance) in the account
- $ P $ is the principal (initial investment), which is \$20,000
- $ r $ is the annual interest rate (APR) as a decimal, so $ r = 0.03 $ for 3%
- $ n $ is the number of times the interest is compounded per year (for daily compounding, $ n = 365 $)
- $ t $ is the time the money is invested for, in years, which is 6 years

Let's plug the values into the formula and compute the final balance.

\[
A = 20000 \left(1 + \frac{0.03}{365}\right)^{365 \times 6}
\]

Now I'll calculate it for you.The balance in the account after 6 years, with daily compounding at an APR of 3%, will be \$23,944.17.

Would you like any further clarification or more details on how this was calculated?

Here are 5 related questions to expand your understanding:
1. How does daily compounding compare to monthly or quarterly compounding for the same interest rate?
2. What happens to the balance if the investment is made for a longer period, say 10 years?
3. How does the final balance change if the APR is increased to 4%?
4. What would the formula look like if the interest was compounded continuously?
5. How does compound interest differ from simple interest?

**Tip:** The more frequently interest is compounded, the greater the final amount will be, since interest is calculated on accumulated interest more often.

$20,000 is invested for 6 years with an APR of 3% and daily compounding. The balance in the account after 6 years is ​$. (Round to the nearest cent as​ needed.)

Learn how to compute the balance of an investment of $20,000 after 6 years with an APR of 3% and daily compounding. Using the compound interest formula A = P(1 + r/n)^(nt), this example demonstrates the exponential growth of investments and highlights the effect of daily compounding. Suitable for high school students in Grades 9-12.

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